To solve a directly proportional situation where percentages are involved, use one of the following strategies, depending on the context.
Calculating the percentage of a number consists of finding the number that corresponds to the desired percentage.
This calculation involves finding the missing term in an equation with fractions where one of the fractions has a denominator of |100|. Basically, the goal is to find the portion of a whole that corresponds to the given percentage. There are several methods for calculating the percentage of a number.
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Method 1: Multiplication by Percentage
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Method 2: Cross Multiplication
To perform this method successfully, it is important to know how to express a percentage in decimal notation.
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Express the percentage in decimal notation.
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Multiply the decimal by the number in order to find n percent of the number.
The results of a poll indicate that |30\ \%| of students of a high school with |1\ 500| students think that the cafeteria menu should be changed.
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Express the percentage in decimal notation ||\displaystyle 30\ \%=\frac{30}{100}=0.3||
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Multiply the decimal by the number in order to find n percent of the number ||0.3\times 1\ 500=450||
So, |450| students want the cafeteria menu changed.
This method is derived from the fundamental property of proportions. It should be noted that several methods can be used to solve a directly proportional situation when calculating the percentage of a number. However, the cross multiplication method is often preferred in situations involving percentages.
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Convert the problem into an equation with two fractions where one of the fractions represents the percentage and the other fraction contains the term with a missing numerator.
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Calculate the percentage of the number using cross multiplication or another method of choice.
In a class of |32| students, |75\ \%| are boys. How many boys are there in the class?
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Convert the problem into an equation with two fractions where one of the fractions represents the percentage and the other fraction contains a term with a missing numerator ||\displaystyle \frac{?\ \text{students}}{32\ \text{students}}=\frac{75}{100}||
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Calculate the percent of the number using cross multiplication ||\begin{align}?\times 100&=32\times 75\\ \\ ?&=\frac{32\times 75}{100}\\ \\ ?&=24\end{align}||
So there are |24| boys in the class of |32| students.
Finding one hundred percent of a number is finding the value that equals |100\ \%| of a set or quantity.
This calculation is carried out using the known number and its corresponding percentage.
Cross multiplication is the preferred method for calculating one hundred percent of a number, but it is possible to perform this calculation using other methods for solving a directly proportional situation.
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Convert the problem into an equation with two fractions where one of the fractions represents a percentage and the other fraction contains a term with a missing denominator (representing one hundred percent of the number).
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Calculate one hundred percent of the number using cross multiplication or any other method of choice.
|64\ \%| of people on a cruise ship speak English. If this percentage corresponds to |800| people who speak English, how many people are there on the ship?
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Convert the problem into an equation with two fractions where one of the fractions represents a percentage and the other fraction contains a term with a missing denominator (representing one hundred percent of the number)
|\color{blue}{64}\ \%| represents |\color{blue}{800}| people. ||\dfrac{\color{blue}{64}}{100}=\dfrac{\color{blue}{800}\ \text{people}}{?\ \text{people}}|| -
Calculate one hundred percent of the number using cross multiplication or any other method of choice ||\begin{align}64\times ?&=100\times 800\\ \\?&=\frac{100\times 800}{64}\\ \\?&=1\ 250\end{align}||
So, there are |1\ 250| people on the cruise ship.
Normand plans to lengthen the dock near his cottage by |20\ \%| this summer. The dock will be |8.4| metres long afterwards.
What is the current length of Normand's dock?
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Convert the problem into an equation with two fractions where one of the fractions represents a percentage and the other fractions contains a term with a missing denominator (representing one hundred percent of the number)
Since Normand lengthens the dock by |20\ \%,| the percentage representing the extended dock is |100\ \% +20\ \% = \color{blue}{120\ \%}|. Therefore, |\color{blue}{120\ \%}| corresponds to |\color{blue}{8.4}\ \text{m}.| ||\dfrac{\color{blue}{120}}{100} = \dfrac{\color{blue}{8.4}\:\text{m}}{?\:\text{m}}|| -
Calculate one hundred percent of the number using cross multiplication or another method of choice ||\begin{align}120\times ?&=100\times 8.4\\ \\?&=\frac{100\times 8{.}4}{120}\\ \\?&=7\end{align}||
The current length of Normand’s dock is |7| metres.